Computing Different Realizations of Linear Dynamical Systems with Embedding Eigenvalue Assignment

In this paper we investigate realizability of discrete time linear dynamical systems (LDSs) in fixed state space dimension. We examine whether there exist different Θ = (A,B,C,D) state space realizations of a given Markov parameter sequence Y with fixed B, C and D state space realization matrices. Full observation is assumed in terms of the invertibility of output mapping matrix C. We prove that the set of feasible state transition matrices associated to a Markov parameter sequence Y is convex, provided that the state space realization matrices B, C and D are known and fixed. Under the same conditions we also show that the set of feasible Metzler-type state transition matrices forms a convex subset. Regarding the set of Metzler-type state transition matrices we prove the existence of a structurally unique realization having maximal number of non-zero off-diagonal entries. Using an eigenvalue assignment procedure we propose linear programming based algorithms capable of computing different state space realizations. By using the convexity of the feasible set of Metzler-type state transition matrices and results from the theory of non-negative polynomial systems, we provide algorithms to determine structurally different realization. Computational examples are provided to illustrate structural non-uniqueness of network-based LDSs.

Kurtosis-based IMM filter for multiple MEMS gyroscopes fusion

Purpose The purpose of this study is to explore a signal processing method to improve the angular rate accuracy of micro-electro-mechanical system (MEMS) gyroscope by combining numerous gyroscopes. Design/methodology/approach To improve the dynamic performance of the signal processing method, the interacting multiple model (IMM) can be applied to the fusion of gyroscope array. However, the standard IMM has constant Markov parameter, which may reduce the model switching speed. To overcome this problem, an adaptive IMM filter is developed based on the kurtosis of the gyroscope output, in which the transition probabilities are adjusted online by utilizing the dynamic information of the rate signal. Findings The experimental results indicate that the precision of the gyroscope array composed of six gyroscopes increases significantly and the kurtosis-based adaptive Markov parameter IMM filter (K-IMM) performs better than the baseline methods, especially under dynamic conditions. These experiments prove the validity of the proposed fusion method. Practical implications The proposed method can improve the accuracy of MEMS gyroscopes without breakthrough on hardware, which is necessary to extend their utility while not restricting the overwhelming advantages. Original/value A K-IMM algorithm is proposed in this paper, which is used to improve the angular rate accuracy of MEMS gyroscope by combining numerous gyroscopes.

WEIGHTS OF MARKOV TRACES OF ALEXANDER POLYNOMIALS FOR MIXED LINKS

Using the Fourier expansion of Markov traces for Ariki–Koike algebras over ℚ(q, u1, …, ue), we give a direct definition of the Alexander polynomials for mixed links. We observe that under the corresponding specialization of a Markov parameter, the Fourier coefficients of Markov traces take quite a simple form. As a consequence, we show that the Alexander polynomial of a mixed link is essentially equal to the Alexander polynomial of the link obtained by resolving the twisted parts.